Non-isothermal diffusion in interconnected discrete-distributed systems: a variational approach

TL;DR

This paper develops a variational framework for non-isothermal diffusion in interconnected systems, deriving generalized interface conditions and flux expressions relevant to engineering and biophysical applications.

Contribution

It introduces a novel variational approach to model non-isothermal diffusion in systems combining distributed and discrete components, leading to new interface conditions.

Findings

Derived generalized Robin interface conditions.

Formulated phenomenological flux expressions.

Provided a variational framework applicable to complex systems.

Abstract

Motivated by compartmental analysis in engineering and biophysical systems, we present a variational framework for the nonequilibrium thermodynamics of systems involving both distributed and discrete (finite dimensional) subsystems by specifically using the ideas of interconnected systems. We focus on the process of non-isothermal diffusion and show how the resulting form of the entropy equation naturally yields phenomenological expressions for the diffusion and entropy fluxes between two compartments, which results in generalized forms of Robin type interface conditions.